28 found
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  1.  25
    Nāgārjunian-Yogācārian Modal Logic versus Aristotelian Modal Logic.Andrew Schumann - 2021 - Journal of Indian Philosophy 49 (3):467-498.
    There are two different modal logics: the logic T assuming contingency and the logic K = assuming logical determinism. In the paper, I show that the Aristotelian treatise On Interpretation has introduced some modal-logical relationships which correspond to T. In this logic, it is supposed that there are contingent events. The Nāgārjunian treatise Īśvara-kartṛtva-nirākṛtiḥ-viṣṇoḥ-ekakartṛtva-nirākaraṇa has introduced some modal-logical relationships which correspond to K =. In this logic, it is supposed that there is a logical determinism: each event happens necessarily or (...)
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  2.  43
    On Two Squares of Opposition: The Leśniewski’s Style Formalization of Synthetic Propositions. [REVIEW]Andrew Schumann - 2013 - Acta Analytica 28 (1):71-93.
    In the paper we build up the ontology of Leśniewski’s type for formalizing synthetic propositions. We claim that for these propositions an unconventional square of opposition holds, where a, i are contrary, a, o (resp. e, i) are contradictory, e, o are subcontrary, a, e (resp. i, o) are said to stand in the subalternation. Further, we construct a non-Archimedean extension of Boolean algebra and show that in this algebra just two squares of opposition are formalized: conventional and the square (...)
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  3.  20
    Non-Archimedean Fuzzy and Probability Logic.Andrew Schumann - 2008 - Journal of Applied Non-Classical Logics 18 (1):29-48.
    In this paper the non-Archimedean multiple-validity is proposed for basic fuzzy logic BL∀∞ that is built as an ω-order extension of the logic BL∀. Probabilities are defined on the class of fuzzy subsets and, as a result, for the first time the non-Archimedean valued probability logic is constructed on the base of BL∀∞.
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  4.  9
    On the Origin of Indian Logic from the Viewpoint of the Pāli Canon.Andrew Schumann - 2019 - Logica Universalis 13 (3):347-393.
    In this paper, I show that in the Pāli Canon there was a tradition of Buddhist logic, but this tradition was weak, and the proto-logic we can reconstruct on the basis of the early Pāli texts can be evaluated as a predecessor of the Hindu logic. According to the textual analysis of the Pāli texts, we can claim that at the time of the closing of the Pāli Canon there did not exist the Nyāya philosophy known by the Nyāya Sūtra. (...)
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  5.  31
    Preface.Andrew Schumann - 2011 - History and Philosophy of Logic 32 (1):1-8.
    In this article, the author attempts to explicate the notion of the best known Talmudic inference rule called qal wa-omer. He claims that this rule assumes a massive-parallel deduction, and for formalizing it, he builds up a case of massive-parallel proof theory, the proof-theoretic cellular automata, where he draws conclusions without using axioms.
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  6.  7
    Legal Argumentation in Mesopotamia Since Ur III.Andrew Schumann - 2020 - Journal of Argumentation in Context 9 (2):243-282.
    In this paper, I show that we can find some foundations of logic and legal argumentation in the tablets of Mesopotamia at least since the dynasty of Ur III. In these texts, we see the oldest correct application of logical inference rules. As concerns the legal argumentation established in Mesopotamia, we can reconstruct on the basis of the tablets the following rules of dispute resolutions during trials: There are two parties of disputants: a protagonist who formulates a standpoint and an (...)
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  7.  19
    Syllogistic System for the Propagation of Parasites. The Case of Schistosomatidae.Andrew Schumann & Ludmila Akimova - 2015 - Studies in Logic, Grammar and Rhetoric 40 (1):303-319.
    In the paper, a new syllogistic system is built up. This system simulates a massive-parallel behavior in the propagation of collectives of parasites. In particular, this system simulates the behavior of collectives of trematode larvae.
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  8.  1
    Judaic Logic.Andrew Schumann (ed.) - 2010 - Gorgias Press.
    Judaic reasoning is discussed from the standpoint of modern logic. Andrew Schumann defines Judaic logic, traces Aristotelian influence on developing Jewish studies in Judaic reasoning, and shows the non-Aristotelian core of fundamentals of Judaic logic. Further, Schumann proposes some modern approaches to understanding and formalizing Judaic reasoning, including Judaic semantics and (non-Aristotelian) syllogistics.
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  9.  52
    A Lattice for the Language of Aristotle's Syllogistic and a Lattice for the Language of Vasiľév's Syllogistic.Andrew Schumann - 2006 - Logic and Logical Philosophy 15 (1):17-37.
    In this paper an algebraic system of the new type is proposed (namely, a vectorial lattice). This algebraic system is a lattice for the language of Aristotle’s syllogistic and as well as a lattice for the language of Vasiľév’s syllogistic. A lattice for the language of Aristotle’s syllogistic is called a vectorial lattice on cap-semilattice and a lattice for the language of Vasiľév’s syllogistic is called a vectorial lattice on closure cap-semilattice. These constructions are introduced for the first time.
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  10.  30
    Qal Wa- Omer and Theory of Massive-Parallel Proofs.Andrew Schumann - 2011 - History and Philosophy of Logic 32 (1):71-83.
    In this article, the author attempts to explicate the notion of the best known Talmudic inference rule called qal wa- omer. He claims that this rule assumes a massive-parallel deduction, and for formalizing it, he builds up a case of massive-parallel proof theory, the proof-theoretic cellular automata, where he draws conclusions without using axioms.
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  11.  21
    Non-Archimedean Valued Predicate Logic.Andrew Schumann - 2007 - Bulletin of the Section of Logic 36 (1/2):67-78.
  12.  17
    Logical Approach to P-Adic Probabilities.A. Yu Khrennikov & Andrew Schumann - 2006 - Bulletin of the Section of Logic 35 (1):49-57.
  13.  8
    The Logic System is the Way You Do Logic.Dov M. Gabbay & Andrew Schumann - 2014 - Studia Humana 3 (4):41-44.
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  14.  3
    Creative Reasoning and Content-Genetic Logic.Andrew Schumann - 2018 - Studia Humana 7 (4):39-47.
    In decision making quite often we face permanently changeable and potentially infinite databases when we cannot apply conventional algorithms for choosing a solution. A decision process on infinite databases is called troubleshooting. A decision on these databases is called creative reasoning. One of the first heuristic semi-logical means for creative decision making were proposed in the theory of inventive problem solving by Genrich Altshuller. In this paper, I show that his approach corresponds to the so-called content-generic logic established by Soviet (...)
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  15. Judgments and Truth: Essays in Honour of Jan Woleński.Andrew Schumann - 2020 - Studia Humana 9 (3-4):1-9.
    It is a Preface to Volume 9:3/4 that has brought a renewed focus to the role of truth conceptions in frameworks of semantics and logic. Jan Woleński is known due to his works on epistemological aspects of logic and his systematization of semantic truth theory. He became the successor and the worthy continuer of prominent Polish logicians: Alfred Tarski and Kazimierz Ajdukiewicz. This volume is collected on the 80th anniversary of Woleński’s birth and draws together new research papers devoted to (...)
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  16.  64
    Logical Cornestones of Judaic Argumentation Theory.Andrew Schumann - 2013 - Argumentation 27 (3):305-326.
    In this paper, the four Judaic inference rules: qal wa- ḥ omer, gezerah š awah, heqe š, binyan ’av are considered from the logical point of view and the pragmatic limits of applying these rules are symbolic-logically explicated. According to the Talmudic sages, on the one hand, after applying some inference rules we cannot apply other inference rules. These rules are weak. On the other hand, there are rules after which we can apply any other. These rules are strong. This (...)
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  17.  2
    Logical Determinacy Versus Logical Contingency. The Case of Łukasiewicz’s Three-Valued Logic.Andrew Schumann - 2019 - Studia Humana 8 (2):8-15.
    In constructing the three-valued logic, Jan Łukasiewicz was highly inspirited by the Aristotelian idea of logical contingency. Nevertheless, we can construct a four-valued logic for explicating the Stoic idea of logical determinacy. In this system, we have the following truth values: 0, 1, 2, 3, where the designated truth value is represented by the two values: 2 and 3.
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  18. Logic in Central and Eastern Europe: History, Science, and Discourse.Andrew Schumann (ed.) - 2012 - Upa.
    This book is a collection of rare material regarding logical and analytic-philosophical traditions in Central and Eastern European countries, covering the period from the late nineteenth century to the early twenty-first century. An encyclopedic feature covers the history of logic and analytic philosophy in all European post-Socialist countries.
     
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  19.  14
    Modal Calculus of Illocutionary Logic.Andrew Schumann - 2010 - In Piotr Stalmaszczyk (ed.), Objects of Inquiry in Philosophy of Language and Linguistics. Ontos Verlag. pp. 261.
  20.  14
    On the Origin of Logical Determinism in Babylonia.Andrew Schumann - 2021 - Logica Universalis 15 (3):331-357.
    In this paper, I show that the idea of logical determinism can be traced back from the Old Babylonian period at least. According to this idea, there are some signs which can explain the appearance of all events. These omens demonstrate the will of gods and their power realized through natural forces. As a result, each event either necessarily appears or necessarily disappears. This idea can be examined as the first version of eternalism – the philosophical belief that each temporal (...)
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  21.  7
    Preface: Ideas and Society on the 150th Anniversary of the Birth of Leon Petrażycki.Andrew Schumann - 2018 - Studia Humana 7 (3):3-4.
    It is a Preface to Volumes 7:3 and 7:4 consisting of articles presented at the International Interdisciplinary Conference Ideas and Society on the 150th anniversary of the birth of Leon Petrażycki, held on November 24, 2017, in Rzeszów, Poland.
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  22. Philosophical Logic.Andrew Schumann (ed.) - 2008 - University of Białystok.
  23. Preface: Philosophical Basis for Making Decisions.Andrew Schumann & Jan Woleński - 2019 - Studia Humana 8 (2):1-2.
    It is a Preface to Volume 8:2 consisting of articles presented at the International Interdisciplinary Conference anniversary of the birth of Jan Łukasiewicz, Rzeszów, Poland.
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  24.  19
    Physarum Polycephalum Syllogistic L-Systems and Judaic Roots of Unconventional Computing.Andrew Schumann - 2016 - Studies in Logic, Grammar and Rhetoric 44 (1):181-201.
    We show that in Kabbalah, the esoteric teaching of Judaism, there were developed ideas of unconventional automata in which operations over characters of the Hebrew alphabet can simulate all real processes producing appropriate strings in accordance with some algorithms. These ideas may be used now in a syllogistic extension of Lindenmayer systems, where we deal also with strings in the Kabbalistic-Leibnizean meaning. This extension is illustrated by the behavior of Physarum polycephalum plasmodia which can implement, first, the Aristotelian syllogistic and, (...)
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  25.  1
    Pragmatic Studies in Judaism.Andrew Schumann, Aviram Ravitsky, Lenn E. Goodman, Furio Biagini, Alan Mittleman, Uri J. Schild, Michael Abraham, Dov Gabbay, Peter Ochs, Yuval Jobani & Tzvee Zahavy (eds.) - 2013 - Gorgias Press.
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  26.  13
    P-Adic Valued Logical Calculi in Simulations of the Slime Mould Behaviour.Andrew Schumann - 2015 - Journal of Applied Non-Classical Logics 25 (2):125-139.
    In this paper we consider possibilities for applying p-adic valued logic BL to the task of designing an unconventional computer based on the medium of slime mould, the giant amoebozoa that looks for attractants and reaches them by means of propagating complex networks. If it is assumed that at any time step t of propagation the slime mould can discover and reach not more than attractants, then this behaviour can be coded in terms of p-adic numbers. As a result, this (...)
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  27.  5
    Reflexive Games in Management.Andrew Schumann - 2018 - Studia Humana 7 (1):44-52.
    In this paper reflexive games are defined as a way to act beyond equilibria to control our opponents by our hiding motives. The task of a reflexive game is to have the opponent’s actions become transparent for us, while our actions remain obscure for the competitor. In case a reflexive game is carried out between agents belonging to the same organisation, success in a reflexive game can be reached by a purposeful modification of some components of a controlled system. Such (...)
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  28.  27
    Towards New Probabilistic Assumptions in Business Intelligence.Andrzej Szelc & Andrew Schumann - 2014 - Studia Humana 3 (4):11-21.
    One of the main assumptions of mathematical tools in science is represented by the idea of measurability and additivity of reality. For discovering the physical universe additive measures such as mass, force, energy, temperature, etc. are used. Economics and conventional business intelligence try to continue this empiricist tradition and in statistical and econometric tools they appeal only to the measurable aspects of reality. However, a lot of important variables of economic systems cannot be observable and additive in principle. These variables (...)
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